The present invention relates generally to global positioning system (GPS) satellite signal acquisition and more specifically to a faster computation algorithm for GPS P(Y) code and multiple blocks C/A code satellite signal acquisition.
The nominal GPS operational constellation consists of 24 satellites that orbit the earth in 12 hours. The control segment consists of tracking stations located around the world. The GPS user segment consists of the GPS receivers and the user community. GPS satellite transmits specially coded satellite signals that can be processed by GPS receivers and provide the information to compute a user's velocity, time and position.
The GPS satellites transmit two microwave carrier signals. FIG. 1 is a prior art drawing of GPS signals. The L1 frequency (1575.42 MHz) shown at 100 carries the navigation message. The L2 frequency represented at 105 (1227.60 MHz) is used to measure the ionospheric delay by precise positioning service equipped receivers. Three binary codes shift the L1 and/or L2 carrier phase.
The Coarse Acquisition Code (C/A) shown at 102 modulates the L1 carrier phase. The C/A code is a repeating 1 MHz Pseudo Random Noise (PRN) Code. This noise-like code modulates the L1 carrier signal, “spreading” the spectrum over a 2 MHz bandwidth. The C/A code repeats every 1023 bits (one millisecond). There is a different C/A code PRN for each GPS satellite. GPS satellites are often identified by their PRN number, the unique identifier for each pseudo-random-noise code. The C/A code that modulates the L1 carrier is the basis for the civil standard positioning service (SPS).
The P-Code (Precise) shown at 104 modulates both the L1 and L2 carrier phases. The P-Code is a very long (seven days) 20 MHz PRN code. In the Anti-Spoofing (AS) mode of operation, the P-Code is encrypted into the Y-Code. The encrypted Y-Code requires a classified AS Module for each receiver. Therefore, only authorized users with cryptographic keys can use it. The P (Y)-Code is the basis for the precise positioning service (PPS).
The navigation message shown at 103 also modulates the L1-C/A code signal. The Navigation Message is a 50 Hz signal consisting of data bits that describe the GPS satellite orbits, clock corrections, and other system parameters.
The C/A code and P(Y) code are code division multiple access (CDMA) systems where a pair of unique signals are assigned to each satellite in the GPS phase of the C/A code or the P(Y) code. The GPS receiver applies correlation to measure timing. The received signal is correlated with the locally generated replicas of the selected satellite's signal. This process is called acquisition. The traditional GPS receiver acquires this phase by continuous sliding, multiplication, and addition. This process is time consuming and is not conducive to miniaturized receivers. The C/A code is used in civilian GPS receivers and the military GPS receivers use both C/A code and P(Y) code. In general, the military receiver acquires the C/A code and transfers this timing to P(Y) code for tracking. However, if the military GPS receiver is under hostile environment and exposed to a strong jamming threat, the less vulnerable direct P(Y) acquisition becomes necessary. The present invention applies to both the C/A code and the P(Y) code to reduce the calculations required to find a weak GPS signal through coherent acquisition.
The conventional P(Y) code acquisition uses a time domain correlation approach as shown in FIG. 2. For each satellite, this approach correlates 10 ms of received sampled data (500,000 data points if sampled at 50 MHz), represented at 200 with 200 locally generated replica, represented at 201. These replica are represented byr(m)=Pj(mΔf)exp(j2πtkmΔt)  (1)where Δt is sampling interval, Pj(mΔt) is the sampled P(Y) code of satellite j, m=0, 1, 2, . . . , 499,999 is a time index, and, fk is the center frequency of the locally generated replica. To acquire the P(Y) code of the received signal from a targeted satellite, 200 locally generated replica are correlated with 500,000 sampled points of the received signal. If any of these 200 correlation result is above the threshold which is pre-determined by the correlation noise floor statistics, the code and the carrier frequency acquisition is completed, as is represented at 202. If none of the results is above the threshold, another 500,000 sampled data will be processed in the same manner, as represented at 203. This new 500,000 data set, represented at 204, only shifts one data point from the previous one. This process continues until either a signal is found or 2 ms of search range is exhausted. For ±1 ms of search range, the average amount of mathematical operations is 200×100,000 500000-point correlation, making the known approach a time consuming and energy consuming operation.
To find a GPS C/A code signal, one need to find its carrier frequency and the beginning of the code. The C/A code is repetitive every millisecond, thus it is adequate to search for 1 ms of data if the signal is reasonably strong. An acquisition method is required to search in both the time and frequency domains. For a high speed aircraft, the expected Doppler frequency range can be +/−10 KHz. Therefore, the acquisition will search 20 KHz for the frequency. Let us assume that the input signal is digitized at 5 MHz. One millisecond of data contains of 5,000 data points.
One way to perform acquisition is through circular correlation in frequency domain. In this approach the following steps are performed.
(a) Generate a group of complex radio frequency (RF) signals according to the length of the data to be processed. This data length should be a multiple number of 1 ms. The frequency of this signal must be +/−10 KHz around the carrier frequency with the frequency resolution equal to 1 over the data length. Perform steps (b) through (g) for each complex radio frequency signal generated in step (a).
(b) Multiply the input signal by one of the complex RF signals. The resultant signal is very close to base band (or zero frequency). The operation can be expressed mathematically ass1(n)=s(n)·rf(n)  (Eq. 1)where s(n) is the digitized input signal and rf(n) is the digitized complex radio frequency (RF) signal in time domain, which can be expressed asrf(n)=ej2ft(n)  (Eq. 2)
(c) Transfer s1 from time domain to frequency domain through the fast Fourier transform (FFT) to frequency domain asS1(k)=FFT[s1(n)]  (Eq. 3)
(d) Take the digitized C/A code of a certain satellite and make them to match the input data length, which is a multiple of ms. Call this signal c(n).
(e) Take the FFT of c(n) and then take the complex conjugate asC(k)={FFT[c(n)]}*  (Eq. 4)Where * represents taking complex conjugate.
(f) Multiply C(k) and S1(k) and take inverse FFT. The result isr(n)=IFFT[S1(k)C(k)]  (Eq. 5)where r(n) is the circular correlation result of s1(n) and c(n).
(g) Take the absolute value of r(n) and find the maximum. If the maximum is greater than the precalculated threshold, the value n of the maximum is the beginning of the C/A code and the RF frequency is the frequency of the carrier.
Consider the description of circular correlation with 1 ms of data. One millisecond of data in time domain can generate 1 KHz resolution in the frequency domain. Therefore, the acquisition program will search the 20 KHz frequency range in 1 KHz steps. There are 21 frequency bins to be searched from −10 KHz to +10 KHz. This approach performs 5,000 point FFT and inverse FFT at each frequency.
Consider the description of circular correlation with 10 ms of data. Ten milliseconds of data digitized at 5 MHz generates 50,000 points. Also, ten milliseconds of data in time domain can generate 100 Hz resolution in the frequency domain. Therefore, the acquisition program will search the 20 KHz frequency range in 100 Hz steps. There are 201 frequency bins to be searched from −10 KHz to +10 KHz. Following the discussion in the previous section, this approach performs 50,000 point FFT and inverse FFT at each frequency. This approach can find weaker GPS signals. One can see that this approach increases the complication of calculation tremendously.
For a GPS receiver with an outside antenna, the signal strength is sufficiently strong such that 1 ms of data can be used for acquisition to find the signal. However, for weak signals, such as placing an antenna indoors, a long record of data is needed for acquisition. The present invention can reduce calculations for acquiring GPS signals using a coherent acquisition method.